Are Metallacyclopentadienes Always Non-Aromatic?

Even though metallacyclopentadienes (MCPs) are among the most common metallacycles, their electron delocalization (aromaticity) has received far less attention than other metallacycles, such as metallabenzenes. We systematically studied the aromaticity of MCPs with energetic (isomerization stabilization energy), density (delocalization index) and magnetic (current density) aromaticity indices. The indices agree that metallacyclopentadienes are, in general, weakly aromatic at most. The 18e− complexes showed the expected weak aromaticity, and only the d8 molecules are somewhat anti-aromatic. However, the theoretical account of the aromaticity of the 16e− MCPs is more convoluted. We find that the aromatic criteria for a 16e−d4 ruthenacyclopentadiene disagree. The lack of agreement shows that significant electron delocalization is not always related to great stability or to strong diatropic currents.

Analysis of current characteristics of transformer bias caused by subway stray current based on measured data

The metro stray current, as the driving source which causes the magnetic bias of the urban network transformer, has the characteristics of rapid change, complex propagation path, and many influencing factors.It’s unknown where the stray current leaks from, and its specific value cannot be obtained through measurement methods.Therefore, this paper studies the characteristics of transformer neutral magnetic current bias based on the measured data and fault recording data in the process of measurement, and analyzes the influence of stray current on transformer in urban network.

Vector Magnetic Current Imaging of an 8 nm Process Node Chip and 3D Current Distributions Using the Quantum Diamond Microscope

The increasing trend for industry adoption of three-dimensional (3D) microelectronics packaging necessitates the development of new and innovative approaches to failure analysis. To that end, our team is developing a tool called the quantum diamond microscope (QDM) that leverages an ensemble of nitrogenvacancy (NV) centers in diamond for simultaneous wide fieldof- view, high spatial resolution, vector magnetic field imaging of microelectronics under ambient conditions [1,2]. Here, we present QDM measurements of two-dimensional (2D) current distributions in an 8 nm process node flip chip integrated circuit (IC) and 3D current distributions in a custom, multi-layer printed circuit board (PCB). Magnetic field emanations from the C4 bumps in the flip chip dominate the QDM measurements, but these prove to be useful for image registration and can be subtracted to resolve adjacent current traces on the micron scale in the die. Vias, an important component in 3D ICs, display only Bx and By magnetic fields due to their vertical orientation, which are challenging to detect with magnetometers that traditionally only measure the Bz component of the magnetic field (orthogonal to the IC surface). Using the multi-layer PCB, we demonstrate that the QDM's ability to simultaneously measure Bx, By, and Bz magnetic field components in 3D structures is advantageous for resolving magnetic fields from vias as current passes between layers. The height difference between two conducting layers is determined by the magnetic field images and agrees with the PCB design specifications. In our initial steps to provide further z depth information for current sources in complex 3D circuits using the QDM, we demonstrate that, due to the linear properties of Maxwell's equations, magnetic field images of individual layers can be subtracted from the magnetic field image of the total structure. This allows for isolation of signal from individual layers in the device that can be used to map embedded current paths via solution of the 2D magnetic inverse. Such an approach suggests an iterative analysis protocol that utilizes neural networks trained with images containing various classes of current sources, standoff distances, and noise integrated with prior information of ICs to subtract current sources layer by layer and provide z depth information. This initial study demonstrates the usefulness of the QDM for failure analysis and points to technical advances of this technique to come.

Chiral magnetic effect and three-point function from AdS/CFT correspondence

The chiral magnetic effect with a fluctuating chiral imbalance is more realistic in the evolution of quark-gluon plasma, which reflects the random gluonic topological transition. Incorporating this dynamics, we calculate the chiral magnetic current in response to space-time dependent axial gauge potential and magnetic field in AdS/CFT correspondence. In contrast to conventional treatment of constant axial chemical potential, the response function here is the AVV three-point function of the $$ \mathcal{N} $$ N = 4 super Yang-Mills at strong coupling. Through an iterative solution of the nonlinear equations of motion in Schwarzschild-AdS5 background, we are able to express the AVV function in terms of two Heun functions and prove its UV/IR finiteness, as expected for $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We found that the dependence of the chiral magnetic current on a non-constant chiral imbalance is non-local, different from hydrodynamic approximation, and demonstrates the subtlety of the infrared limit discovered in field theoretic approach. We expect our results enrich the understanding of the phenomenology of the chiral magnetic effect in the context of relativistic heavy ion collisions.

The Dimension of Phaseless Near-Field Data by Asymptotic Investigation of the Lifting Operator

In this paper, the question of evaluating the dimension of data space in an inverse source problem from near-field phaseless data is addressed. The study is developed for a 2D scalar geometry made up by a magnetic current strip whose square magnitude of the radiated field is observed in near non-reactive zone on multiple lines parallel to the source. With the aim of estimating the dimension of data space, at first, the lifting technique is exploited to recast the quadratic model as a linear one. After, the singular values decomposition of such linear operator is introduced. Finally, the dimension of data space is evaluated by quantifying the number of “relevant” singular values. In the last part of the article, some numerical simulations that corroborate the analytical estimation of data space dimension are shown.

Unified Theory of Gravity and Electromagnetism: Classical and Quantum Aspects

A unified classical theory of gravity and electromagnetism with a torsion vector 0, proposed by S N Bose in 1952, is introduced. In this theory, the torsion vector acts as a magnetic current and it is shown that (i) the electromagnetism is invariant under continuous Heaviside–Larmor transformations and (ii) the electric and magnetic charges are topologically quantised, satisfying the Dirac quantisation condition, without implying any Dirac string provided is curl-less.